The timeline of particle discoveries actually extends all the way back to William Herschel, who discovered infrared, known at the time as "heat rays."
It was early 1800 and Herschel had been studying sunlight. He detected with a thermometer, a one degree difference in temperature beyond the red end of the spectrum when sunlight had been passed through a prism.
Johann Wilhelm Ritter, in 1801, worked the other end of the spectrum, discovering Ultraviolet radiation in the process. These rays were effective at lightening silver chloride-soaked paper.
Both of these "heat rays" and "de-oxidizing rays" were later discovered to be photons. The X-Ray was discovered in Rontgen in 1895 and the Gamma ray in 1900 by Paul Villard.
The first to verifiably discover a particle that we accept in the current Standard Model was J. J. Thompson, who discovered the electron in 1897.
It was previously accepted that atoms were built up from a smallest constituent unit, but that unit was the hydrogen atom, with no further division.
Thompson's work was revolutionary since he proposed a constituent that was about 1000 times smaller than the atom itself. A subatomic particle: the electron.
It was through Thompson's work on the cathode ray, through which the electron was discovered.
Thompson showed that the ray was actually composed of an unknown negatively charged particle.
These particles were 1800 times lighter than the hydrogen atom.
Rutherford, in his alpha particle scattering experiment, which provided experimental confirmation for the atomic nucleus, also utilized the experimental evidence for the alpha particle, discovered earlier, which is essentially a helium nucleus of 2 protons and 2 neutrons. Rutherford discovered the alpha particle actually years earlier, in uranium radiation, in the year 1899. The nucleus was discovered when Rutherford analysed the results of Marsden and Geiger on scattering.
Chadwick
Rutherford also discovered the proton in 1919, while the neutron was not discovered until 1932 by James Chadwick.
The question also persisted of whether the neutron was a composite of a proton and an electron for some few years after the neutron was discovered.
In 1932, Carl D. Anderson discovers the antimatter counterpart of the electron, the positron, though it was not thus named at the time. This was the first antiparticle discovered. A positron has the same mass and spin as an electron, but with opposite or positive charge (electrons are negatively charged.)